[HEG] Observers seeing gravitational Hilbert spaces: abstract sources for an abstract path integral

Who: Vincent Chen (UCSB) 

When: Thursday, November 6, 2pm
Where: KITP Simons Amphitheater

Title: Observers seeing gravitational Hilbert spaces: abstract sources for an abstract path integral
Abstract: The gravitational path integral suggests a striking result: the Hilbert space of closed universes in each superselection sector, a so-called alpha-sector, is one-dimensional. We develop an abstract formalism encapsulating recent proposals that modify the gravitational path integral in the presence of observers and allow larger Hilbert spaces to be associated with closed universes. Our formalism regards the gravitational path integral as a map from abstract objects called sources to complex numbers, and introduces additional objects called partial sources, which form sources when glued together. We apply this formalism to treat, on equal footing, universes with spatial boundaries, closed universes with prescribed observer worldlines, and closed universes containing observers entangled with external systems. In these contexts, the relevant gravitational Hilbert spaces contain states prepared by partial sources and can consequently have nontrivial alpha-sectors supporting noncommuting operators. Within our general framework, the positivity of the gravitational inner product implies a bound on the Hilbert space trace of certain positive operators over each alpha-sector. The trace of such operators, in turn, quantifies the effective size of this Hilbert space. This talk is based on arXiv:2505.15892 [hep-th].